What is expand ((x^2-a)^3)/(ax) ?

The solution to expand ((x^2-a)^3)/(ax) is (x^5)/a-3x^3+3ax-(a^2)/x

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expand ((x^2-a)^3)/(ax)

expand

\frac{( x ^{2} - a ) ^{3}}{a x}

\frac{x ^{5}}{a} - 3 x^{3} + 3 a x - \frac{a ^{2}}{x}

Solution steps

\frac{( x ^{2} - a ) ^{3}}{a x}

(x^{2} - a)^{3} = x^{6} - 3 a x^{4} + 3 a^{2} x^{2} - a^{3}

= \frac{x ^{6} - 3 a x ^{4} + 3 a ^{2} x ^{2} - a ^{3}}{a x}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{6} - 3 a x ^{4} + 3 a ^{2} x ^{2} - a ^{3}}{a x} = \frac{x ^{6}}{a x} - \frac{3 a x ^{4}}{a x} + \frac{3 a ^{2} x ^{2}}{a x} - \frac{a ^{3}}{a x}

= \frac{x ^{6}}{a x} - \frac{3 a x ^{4}}{a x} + \frac{3 a ^{2} x ^{2}}{a x} - \frac{a ^{3}}{a x}

\frac{x ^{6}}{a x} = \frac{x ^{5}}{a}

\frac{3 a x ^{4}}{a x} = 3 x^{3}

\frac{3 a ^{2} x ^{2}}{a x} = 3 a x

\frac{a ^{3}}{a x} = \frac{a ^{2}}{x}

= \frac{x ^{5}}{a} - 3 x^{3} + 3 a x - \frac{a ^{2}}{x}

(x + x^{- 1})^{3}

f (x) = - x + \frac{1}{x} + 1

\frac{d}{d x} (\frac{2}{1 - x ^{3}})

\frac{d}{d x} (e^{- \frac{5}{x}})

\int x (3 x + 1) d x

What is expand ((x^2-a)^3)/(ax) ?
The solution to expand ((x^2-a)^3)/(ax) is (x^5)/a-3x^3+3ax-(a^2)/x